共查询到20条相似文献,搜索用时 0 毫秒
1.
Kailash C. Misra 《代数通讯》2013,41(4):1599-1614
2.
Georgia Benkart Seok-Jin Kang Hyeonmi Lee Kailash C. Misra Dong-Uy Shin 《Compositio Mathematica》2001,126(1):91-111
We prove that the multiplicity of an arbitrary dominant weight for an irreducible highest weight representation of the affine Kac–Moody algebra A
(1)
r
is a polynomial in the rank r. In the process we show that the degree of this polynomial is less than or equal to the depth of the weight with respect to the highest weight. These results allow weight multiplicity information for small ranks to be transferred to arbitrary ranks. 相似文献
3.
Local Weyl modules were originally defined for affine Lie algebras by Chari and Pressley in [5]. In this paper we extend the notion of local Weyl modules for a Lie algebra 𝔤 ?A, where 𝔤 is any Kac–Moody algebra and A is any finitely generated commutative associative algebra with unit over ?, and prove a tensor product decomposition theorem which generalizes result in [2, 5]. 相似文献
4.
Wayne Neidhardt 《Algebras and Representation Theory》1998,1(2):161-168
We prove the following result for a not necessarily symmetrizable Kac–Moody algebra: Let x,y W with x y, and let P+. If n=l(x)-l(y), then Ext C()
n
(M(x·),L(y·))=1. 相似文献
5.
6.
We study the universal enveloping associative conformal algebra for the central extension of a current Lie conformal algebra at the locality level N =?3. A standard basis of defining relations for this algebra is explicitly calculated. As a corollary, we find a linear basis of the free commutative conformal algebra relative to the locality N =?3 on the generators.
相似文献7.
Zhengxin Chen 《代数通讯》2013,41(8):3297-3324
8.
Nitu Kitchloo 《Mathematische Zeitschrift》2014,276(3-4):727-756
We study the topology of spaces related to Kac–Moody groups. Given a Kac–Moody group over $\mathbb C $ , let $\text {K}$ denote the unitary form with maximal torus ${{\mathrm{T}}}$ having normalizer ${{\mathrm{N}}}({{\mathrm{T}}})$ . In this article we study the cohomology of the flag manifold $\text {K}/{{{\mathrm{T}}}}$ as a module over the Nil-Hecke algebra, as well as the (co)homology of $\text {K}$ as a Hopf algebra. In particular, if $\mathbb F $ has positive characteristic, we show that $\text {H}_*(\text {K},\mathbb F )$ is a finitely generated algebra, and that $\text {H}^*(\text {K},\mathbb F )$ is finitely generated only if $\text {K}$ is a compact Lie group . We also study the stable homotopy type of the classifying space $\text {BK}$ and show that it is a retract of the classifying space $\text {BN(T)}$ of ${{\mathrm{N}}}({{\mathrm{T}}})$ . We illustrate our results with the example of rank two Kac–Moody groups. 相似文献
9.
《代数通讯》2013,41(11):5467-5479
Abstract In this paper, we generalize the concept of purely imaginary roots of Kac–Moody algebras to generalized Kac–Moody algebras. Also we give a complete classification of those generalized Kac–Moody algebras with the purely imaginary property. We also define a new class of indefinite non-hyperbolic generalized Kac–Moody algebras called extended hyperbolic generalized Kac–Moody algebras and find that it does not always possess the purely imaginary property whereas the extended hyperbolic Kac–Moody algebras possess the purely imaginary property. 相似文献
10.
Jonathan Brundan 《Mathematische Annalen》2016,364(1-2):353-372
11.
We analyze the extent to which a quantum universal enveloping algebra of a Kac–Moody algebra g is defined by multidegrees of its defining relations. To this end, we consider a class of character Hopf algebras defined by the same number of defining relations of the same degrees as the Kac–Moody algebra g. We demonstrate that if the generalized Cartan matrix A of g is connected then the algebraic structure, up to a finite number of exceptional cases, is defined by just one “continuous” parameter q related to a symmetrization of A, and one “discrete” parameter m related to the modular symmetrizations of A. The Hopf algebra structure is defined by n(n−1)/2 additional “continuous” parameters. We also consider the exceptional cases for Cartan matrices of finite or affine types in more detail, establishing the number of exceptional parameter values in terms of the Fibonacci sequence. 相似文献
12.
In this paper we consider the hyperbolic Kac–Moody algebra $\mathcal {F}$ associated with the generalized Cartan matrix . Its connection to Siegel modular forms of genus 2 was first studied by A. Feingold and I. Frenkel. The denominator function of $\mathcal{F}$ is not an automorphic form. However, Gritsenko and Nikulin extended $\mathcal{F}$ to a generalized Kac–Moody algebra whose denominator function is a Siegel modular form. Using the Borcherds denominator identity, the denominator function can be written as an infinite product. The exponents that appear in the product are given by Fourier coefficients of a weak Jacobi form. P. Niemann also constructed a generalized Kac–Moody algebra which contains $\mathcal {F}$ and whose denominator function is related to a product of Dedekind η-functions. In particular, root multiplicities of the generalized Kac–Moody algebra are determined by Fourier coefficients of a modular form. As the main results of this paper, we compute asymptotic formulas for these Fourier coefficients using the method of Hardy–Ramanujan–Rademacher, and obtain an asymptotic bound for root multiplicities of the algebra $\mathcal{F}$ . Our method can be applied to other hyperbolic Kac–Moody algebras and to other modular forms as demonstrated in the later part of the paper. 相似文献
13.
We show that the quiver Hecke superalgebras and their cyclotomic quotients provide a supercategorification of quantum Kac–Moody algebras and their integrable highest weight modules. 相似文献
14.
This paper is a continuation of the series of papers “Quantization of Lie bialgebras (QLB) I-V”. We show that the image of a Kac-Moody Lie bialgebra with the standard quasitriangular structure under the quantization functor defined in QLB-I,II is isomorphic to the Drinfeld-Jimbo quantization of this Lie bialgebra, with the standard quasitriangular structure. This implies that when the quantization parameter is formal, then the category O for the quantized Kac-Moody algebra is equivalent, as a braided tensor category, to the category O over the corresponding classical Kac-Moody algebra, with the tensor category structure defined by a Drinfeld associator. This equivalence is a generalization of the functor constructed previously by G. Lusztig and the second author. In particular, we answer positively a question of Drinfeld whether the characters of irreducible highest weight modules for quantized Kac-Moody algebras are the same as in the classical case. Moreover, our results are valid for the Lie algebra $\mathfrak{g}(A)$ corresponding to any symmetrizable matrix A (not necessarily with integer entries), which answers another question of Drinfeld. We also prove the Drinfeld-Kohno theorem for the algebra $\mathfrak{g}(A)$ (it was previously proved by Varchenko using integral formulas for solutions of the KZ equations). 相似文献
15.
We investigate regular hyperbolic subalgebras of hyperbolic Kac–Moody algebras via their Weyl groups. We classify all subgroup
relations between Weyl groups of hyperbolic Kac–Moody algebras, and show that for every pair of a group and subgroup there
exists at least one corresponding pair of algebra and subalgebra. We find all types of regular hyperbolic subalgebras for
a given hyperbolic Kac–Moody algebra, and present a finite algorithm classifying all embeddings. 相似文献
16.
《Journal of Pure and Applied Algebra》2002,166(1-2):105-123
We prove a character formula of Kac–Wakimoto type for generalized Kac–Moody algebras. A character formula of this type is a generalization of the Weyl–Kac character formula, and is proved by Kac–Wakimoto in the case of Kac–Moody algebras. We remark that the formula is a generalization of that of Kac–Wakimoto even in the case of Kac–Moody algebras of indefinite type. 相似文献
17.
In this article, we consider all generalized Kac–Moody algebras (GKM algebras) for the purpose of finding out special imaginary roots and strictly imaginary roots. We give a complete classification of GKM algebras possessing special imaginary roots and also give a complete classification of GKM algebras possessing strictly imaginary property (GKM algebras whose imaginary roots are strictly imaginary). We also conclude that the Monster Lie algebra has no special imaginary root and does not satisfy strictly imaginary property. 相似文献
18.
The present paper develops a general theory of quantum group analogs of symmetric pairs for involutive automorphism of the second kind of symmetrizable Kac–Moody algebras. The resulting quantum symmetric pairs are right coideal subalgebras of quantized enveloping algebras. They give rise to triangular decompositions, including a quantum analog of the Iwasawa decomposition, and they can be written explicitly in terms of generators and relations. Moreover, their centers and their specializations are determined. The constructions follow G. Letzter's theory of quantum symmetric pairs for semisimple Lie algebras. The main additional ingredient is the classification of involutive automorphisms of the second kind of symmetrizable Kac–Moody algebras due to Kac and Wang. The resulting theory comprises various classes of examples which have previously appeared in the literature, such as q-Onsager algebras and the twisted q-Yangians introduced by Molev, Ragoucy, and Sorba. 相似文献
19.
Journal of Algebraic Combinatorics - The dual space of the Cartan subalgebra in a Kac–Moody algebra has a partial ordering defined by the rule that two elements are related if and only if... 相似文献